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Modeling Precious Metal Returns through Fractional Jump-Diffusion Processes Combined with Markov Regime-Switching Stochastic Volatility

Author

Listed:
  • Martha Carpinteyro

    (Sección de Estudios de Posgrado, Instituto Politécnico Nacional, 11350 Mexico, Mexico)

  • Francisco Venegas-Martínez

    (Escuela Superior de Economía, Instituto Politécnico Nacional, 11350 Mexico, Mexico)

  • Alí Aali-Bujari

    (Escuela Superior de Apan, Universidad Autónoma de Estado de Hidalgo, 42082 Pachuca, Mexico)

Abstract

This paper is aimed at developing a stochastic volatility model that is useful to explain the dynamics of the returns of gold, silver, and platinum during the period 1994–2019. To this end, it is assumed that the precious metal returns are driven by fractional Brownian motions, combined with Poisson processes and modulated by continuous-time homogeneous Markov chains. The calibration is carried out by estimating the Jump Generalized Autoregressive Conditional Heteroscedasticity (Jump-GARCH) and Markov regime-switching models of each precious metal, as well as computing their Hurst exponents. The novelty in this research is the use of non-linear, non-normal, multi-factor, time-varying risk stochastic models, useful for an investors’ decision-making process when they intend to include precious metals in their portfolios as safe-haven assets. The main empirical results are as follows: (1) all metals stay in low volatility most of the time and have long memories, which means that past returns have an effect on current and future returns; (2) silver and platinum have the largest jump sizes; (3) silver’s negative jumps have the highest intensity; and (4) silver reacts more than gold and platinum, and it is also the most volatile, having the highest probability of intensive jumps. Gold is the least volatile, as its percentage of jumps is the lowest and the intensity of its jumps is lower than that of the other two metals. Finally, a set of recommendations is provided for the decision-making process of an average investor looking to buy and sell precious metals.

Suggested Citation

  • Martha Carpinteyro & Francisco Venegas-Martínez & Alí Aali-Bujari, 2021. "Modeling Precious Metal Returns through Fractional Jump-Diffusion Processes Combined with Markov Regime-Switching Stochastic Volatility," Mathematics, MDPI, vol. 9(4), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:407-:d:502051
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    References listed on IDEAS

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    2. Benjamín Vallejo-Jiménez & Francisco Venegas-Martínez & Oscar V. De la Torre-Torres & José Álvarez-García, 2022. "Simulating Portfolio Decisions under Uncertainty When the Risky Asset and Short Rate Are Modulated by an Inhomogeneous and Asset-Dependent Markov Chain," Mathematics, MDPI, vol. 10(16), pages 1-14, August.

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